The graph shows the variation of velocity of a rocket with time. The maximum height attained by the rocket is ........... $km$ :-

Among the following,the velocity $(v)$ - time $(t)$ graph representing the motion of a vertically projected body is

Two trains, which are moving along different tracks in opposite directions, are put on the same track by mistake. On noticing the mistake, when the trains are $300 \, m$ apart, the drivers start slowing down the trains. The graphs given below show the decrease in their velocities as a function of time. The separation between the trains when both have stopped is: (in $ \, m$)

The velocity-displacement graph of a particle is shown in the figure.
$(a)$ Write the relation between $v$ and $x$.
$(b)$ Obtain the relation between acceleration and displacement and plot it.

Which of the following speed-time $(v-t)$ graphs is physically not possible?

The velocity $(v)$ - distance $(x)$ graph is shown in the figure. Which graph represents the acceleration $(a)$ versus distance $(x)$ variation of this system?